ArticleOriginal scientific text
Title
Hyperelliptic modular curves X₀*(N) with square-free levels
Authors 1, 1
Affiliations
- Department of Mathematics, Waseda University, 3-4-1, Okubo Shinjuku-ku, Tokyo 169, Japan
Bibliography
- A. O. L. Atkin and J. Lehner, Hecke operators on Γ₀(m), Math. Ann. 185 (1970), 134-160.
- A. O. L. Atkin and D. J. Tingley, Numerical tables on elliptic curves, in: Modular Functions of One Variable IV, B. Birch and W. Kuyk (eds.), Lecture Notes in Math. 476, Springer, Berlin, 1975, 74-144.
- P. Deligne et M. Rapoport, Les schémas de modules de courbes elliptiques, in: Modular Functions of One Variable II, P. Deligne and W. Kuyk (eds.), Lecture Notes in Math. 349, Springer, Berlin, 1973, 143-316.
- M. Eichler, The basis problem for modular forms and the traces of the Hecke operators, in: Modular Functions of One Variable I, W. Kuyk (ed.), Lecture Notes in Math. 320, Springer, Berlin, 1973, 75-151.
- R. Hartshorne, Algebraic Geometry, Grad. Texts in Math. 52, Springer, New York, 1977.
- Y. Hasegawa, Table of quotient curves of modular curves X₀(N) with genus 2, Proc. Japan Acad. Ser. A 71 (1995), 235-239.
- K. Hashimoto, On Brandt matrices of Eichler orders, Mem. School Sci. Engrg. Waseda Univ. 59 (1995), 143-165.
- H. Hijikata, Explicit formula of the traces of Hecke operators for Γ₀(N), J. Math. Soc. Japan 26 (1974), 56-82.
- J. Igusa, Kroneckerian model of fields of elliptic modular functions, Amer. J. Math. 81 (1959), 561-577.
- P. G. Kluit, Hecke operators on Γ*(N) and their traces , Dissertation of Vrije Universiteit, Amsterdam, 1979.
- J. Lehner and M. Newman, Weierstrass points of Γ₀(N), Ann. of Math. 79 (1964), 360-368.
- N. Murabayashi, On normal forms of modular curves of genus 2, Osaka J. Math. 29 (1992), 405-418.
- A. P. Ogg, Hyperelliptic modular curves, Bull. Soc. Math. France 102 (1974), 449-462.
- A. P. Ogg, Modular functions, in: The Santa Cruz Conference on Finite Groups, B. Cooperstein and G. Mason (eds.), Proc. Sympos. Pure Math. 37, Amer. Math. Soc., Providence, R.I., 1980, 521-532.
- A. Pizer, An algorithm for computing modular forms on Γ₀(N), J. Algebra 64 (1980), 340-390.
- G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Iwanami Shoten and Princeton Univ. Press, 1971.
- M. Yamauchi, On the traces of Hecke operators for a normalizer of Γ₀(N), J. Math. Kyoto Univ. 13 (1973), 403-411.